Now, although last week's data were slightly encouraging, economists are still hesistant to say initial claims are completely back on track, because the data can be volatile.

"It's way too early to tell," said Jennifer Lee, senior economist with BMO Capital Markets. "There's still so much uncertainty out there and economic growth is still very subpar. If it does continue to improve, it would be very moderate."

Earlier in the month, Minnesota's shutdown caused an upward blip in the numbers, but that proved only temporary after the state government passed a budget on July 20.

Overall, the four-week moving average of initial claims --calculated to smooth out volatility -- fell by 8,500 to 413,750 in the latest week.

Continuing claims -- which include people filing for the second week of benefits or more -- fell to 3,703,000 in the week ended July 16, the most recent data available. That was slightly more than economists' forecasts for 3,688,000.